[✓] Write a matrix multiplication with indefinite limits?

Hello, I need to find an answer to this problem. Let G(t) be a nxn matrix. I need to calculate G(t-1)xG(t-2)x...xG(2)xG(1) where x is the usual matrix multiplication. I can't use the function Product[G(i),{i,t-1,1}] because it uses the usual multiplication of real numbers. Any Idea of how can I solve this?

I'm sorry, I guess I've not been clear. I need to calculate (not only for display) G(t-1)xG(t-2)x...xG(2)xG(1) without setting any value to t. For instance, the product x(x-1)...*(x-t) is equal to Gamma(x+1)/Gamma(x-t). I want to find a closed expression that would depend on t.

what I need is the expression in "Out[249]", this is what I mean by "closed expression". Look that the boundary I've used is an unapropriate bound to a Table or to a loop, but it's not to the function "Product". I'm looking for a function that would do the same thing as the function Product but instead of using the usual multiplication of real numbers, it uses the usual matrix product.